2,699 research outputs found
Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates
We study the motion of a vortex dipole in a Bose-Einstein condensate confined
to an anisotropic trap. We focus on a system of ordinary differential equations
describing the vortices' motion, which is in turn a reduced model of the
Gross-Pitaevskii equation describing the condensate's motion. Using a sequence
of canonical changes of variables, we reduce the dimension and simplify the
equations of motion. We uncover two interesting regimes. Near a family of
periodic orbits known as guiding centers, we find that the dynamics is
essentially that of a pendulum coupled to a linear oscillator, leading to
stochastic reversals in the overall direction of rotation of the dipole. Near
the separatrix orbit in the isotropic system, we find other families of
periodic, quasi-periodic, and chaotic trajectories. In a neighborhood of the
guiding center orbits, we derive an explicit iterated map that simplifies the
problem further. Numerical calculations are used to illustrate the phenomena
discovered through the analysis. Using the results from the reduced system we
are able to construct complex periodic orbits in the original, partial
differential equation, mean-field model for Bose-Einstein condensates, which
corroborates the phenomenology observed in the reduced dynamical equations
Families of Matter-Waves for Two-Component Bose-Einstein Condensates
We produce several families of solutions for two-component nonlinear
Schr\"{o}dinger/Gross-Pitaevskii equations. These include domain walls and the
first example of an antidark or gray soliton in the one component, bound to a
bright or dark soliton in the other. Most of these solutions are linearly
stable in their entire domain of existence. Some of them are relevant to
nonlinear optics, and all to Bose-Einstein condensates (BECs). In the latter
context, we demonstrate robustness of the structures in the presence of
parabolic and periodic potentials (corresponding, respectively, to the magnetic
trap and optical lattices in BECs).Comment: 6 pages, 4 figures, EPJD in pres
Guiding chemical pulses through geometry: Y-junctions
We study computationally and experimentally the propagation of chemical
pulses in complex geometries.The reaction of interest, CO oxidation, takes
place on single crystal Pt(110) surfaces that are microlithographically
patterned; they are also addressable through a focused laser beam, manipulated
through galvanometer mirrors, capable of locally altering the crystal
temperature and thus affecting pulse propagation. We focus on sudden changes in
the domain shape (corners in a Y-junction geometry) that can affect the pulse
dynamics; we also show how brief, localized temperature perturbations can be
used to control reactive pulse propagation.The computational results are
corroborated through experimental studies in which the pulses are visualized
using Reflection Anisotropy Microscopy.Comment: submitted to Phys. Rev.
Discrete surface solitons in two dimensions
We investigate fundamental localized modes in 2D lattices with an edge
(surface). Interaction with the edge expands the stability area for ordinary
solitons, and induces a difference between perpendicular and parallel dipoles;
on the contrary, lattice vortices cannot exist too close to the border.
Furthermore, we show analytically and numerically that the edge stabilizes a
novel wave species, which is entirely unstable in the uniform lattice, namely,
a "horseshoe" soliton, consisting of 3 sites. Unstable horseshoes transform
themselves into a pair of ordinary solitons.Comment: 6 pages, 4 composite figure
A quasi-diagonal approach to the estimation of Lyapunov spectra for spatio-temporal systems from multivariate time series
We describe methods of estimating the entire Lyapunov spectrum of a spatially
extended system from multivariate time-series observations. Provided that the
coupling in the system is short range, the Jacobian has a banded structure and
can be estimated using spatially localised reconstructions in low embedding
dimensions. This circumvents the ``curse of dimensionality'' that prevents the
accurate reconstruction of high-dimensional dynamics from observed time series.
The technique is illustrated using coupled map lattices as prototype models for
spatio-temporal chaos and is found to work even when the coupling is not
strictly local but only exponentially decaying.Comment: 13 pages, LaTeX (RevTeX), 13 Postscript figs, to be submitted to
Phys.Rev.
Reply by A. Carretero et al.
Dear Editor,
The study of vascular casts in the embryo by means of the scanning electron microscope represents the main subject of our research. We fully agree with DeRuiter and Gittenberger-de Groot in that corrosion casting is a valuable tool to study the early angiogenesis in embryos
Technical Improvements in Corrosion Casting of Small Specimens: A Study on Mesonephric Tubules and Vessels of Chicken Embryos
The injection technique for corrosion casting of small, embryonic material can be improved by using a chemical ligature (cyanocrylate). With this simple method, leakage of the resin at the injection site is prevented and the mechanical stability of the cannula-vessel coupling is improved.
The blood vascular system of chicken embryos as small as Hamburger-Hamilton stage 24 (approximately 4.5 days of incubation) has successfully been injected using this procedure. Corrosion casts of the mesonephric tubular system have been made in a similar manner. Additionally, a simple way for secure transport of the fragile casts by immersion in 10% gelatin is suggested
Dynamic and Energetic Stabilization of Persistent Currents in Bose-Einstein Condensates
We study conditions under which vortices in a highly oblate harmonically
trapped Bose-Einstein condensate (BEC) can be stabilized due to pinning by a
blue-detuned Gaussian laser beam, with particular emphasis on the potentially
destabilizing effects of laser beam positioning within the BEC. Our approach
involves theoretical and numerical exploration of dynamically and energetically
stable pinning of vortices with winding number up to , in correspondence
with experimental observations. Stable pinning is quantified theoretically via
Bogoliubov-de Gennes excitation spectrum computations and confirmed via direct
numerical simulations for a range of conditions similar to those of
experimental observations. The theoretical and numerical results indicate that
the pinned winding number, or equivalently the winding number of the superfluid
current about the laser beam, decays as a laser beam of fixed intensity moves
away from the BEC center. Our theoretical analysis helps explain previous
experimental observations, and helps define limits of stable vortex pinning for
future experiments involving vortex manipulation by laser beams.Comment: 8 pages 5 figure
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